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**ABSOLUTE VALUE**

There are several ways to look at the absolute value concept. One way is to consider the absolute value as the

**distance**

from the center of the number line to a given point. The center of the number line is the number

**zero**

. Since distance is always positive, we report the distance from zero to any point as a

**positive**

number. When asked what is the distance from Chicago to St.

Louis, you don't hear people say several hundred negative miles, do you? So

**distance numbers**

are

**positive numbers**

.

For example,

How "far" is it from 0 to the number 15? Answer: 15 units

** -------------------0**

---------------

**15**

How "far" is it from 0 to the number -15? Answer: 15 units

**-**

**15**

---------------

**0------------------**

Using the absolute value notation:

This leads into another way of looking at absolute values.

The absolute value is a

**function.**

You put a number into it, and the number pops out

**positive**

.

If x is a negative number, change the sign of x and write the result.

If x is a positive number, don't change its sign. Write it as it is.

Change the sign of -15 and write the result: 15.

There is no need to change the sign. Just write the number 15.

The way we write "x is a negative number" is like this : x < 0.

"x is positive" is written as x > 0. If we include zero here, we write x > 0.

Hence, we can write the absolute value function like this:

It still works the same way as before, if x is a negative number, change its sign. Don't change the sign if x is positive.